Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches
Abstract
1. Introduction
2. Geometric View of the Likelihood Ratio
3. Analytic Marginalisation of the Likelihood Ratio
3.1. Marginalisation over
3.2. Marginalisation over
4. Receiver–Operator Curves
- (i)
- fixed , (i.e., the neutron star is viewed “edge-on”), ;
- (ii)
- fixed , 3 (i.e., the neutron star is viewed “face-on”), ;
- (iii)
- fixed , randomly drawn , ; and
- (iv)
- fixed , randomly drawn , ;
5. Discussion
Funding
Acknowledgments
Conflicts of Interest
1. | The dot product henceforth denotes the contraction of the last index of the tensor with the first index of the tensor . |
2. | It is common in the literature to quote values of twice the -statistic, i.e., . This convention is not followed in this paper, however. |
3. | This choice of follows that of [36]. |
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Wette, K. Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches. Universe 2021, 7, 174. https://doi.org/10.3390/universe7060174
Wette K. Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches. Universe. 2021; 7(6):174. https://doi.org/10.3390/universe7060174
Chicago/Turabian StyleWette, Karl. 2021. "Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches" Universe 7, no. 6: 174. https://doi.org/10.3390/universe7060174
APA StyleWette, K. (2021). Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches. Universe, 7(6), 174. https://doi.org/10.3390/universe7060174